There have been reports that Sherwood's job was under threat after the club's American owner Randy Lerner met Villa officials in the United States this week.
With the team in the bottom three and facing an away game with champions Chelsea on Saturday, Sherwood told a news conference that he felt it was more important to stay in England and work with the players.
"My object this season was to stay in the Premier League and I'm 100 percent certain we will," he said.
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"The players know the last few weeks haven't been good enough. There are a lot of points to be played for, enough to stay in the division."
Villa bought 13 new players in the close-season but spent only 4.4 million pounds ($6.80 million) net, after receiving big fees when Christian Benteke and Fabian Delph were sold to Liverpool and Manchester City respectively.
Sherwood denied that there were any of the newcomers that he did not want, adding, "I've got to believe in the players that I've got, which I do."
He suggested the fans who were singing his name a few weeks ago would soon "be doing so again", but also acknowledged that he faced dismissal if results did not improve.
"If you don't win games as a football manager, you get sacked," he said.
"I take full responsibility for results. I'm not hiding. I'm standing on the touchline taking the brunt of it."
(Reporting by Steve Tongue; editing by Toby Davis)
